I distinctly remember seeing in a blue book a chart illustrating the fact that verb conjugations for v5 verbs follow the a/i/u/e/o pattern -- that is, the negative stem, masu stem, plain form, conditional stem and er, er, intentional (?) stem are formed just like the syllabary column of the verb's last syllable.
Maybe I am weird, but for me this INSTANTLY made the whole system much more understandable. Then of course, I had to learn v1 verbs like taberu, but I thought of them as just a simplified version of the v5 pattern.
I have no idea if conjugation is commonly taught this way, since I've never taken an organized class in Japanese. But for me it turned chaos into order in a single instant.
This is why they are called v5/v1 or 五段動詞/一段動詞 5 step verbs/1 step verbs.
5 step verbs use all the a/i/u/e/o for negative/stem(noun)/plain, dictionary form/command, conditional/volitional. v1 just drops the ru in any conjugation.
The terms category 1, 2, and 3 never made any logical sense to me and was never used when I studied in Japan.
I agree that polite form should be stressed in beginning level classes, but teaching conjugation from dictionary form to masu form taking at most 2 class meetings. I am pretty sure every Japanese book I've studied from made it clear that using the plain form in inappropriate times can be rude.